1. TARGETS 4-6 Isosceles and Equilateral Triangles (Pg .283)
Use properties of isosceles triangles.
Use properties of equilateral triangles. `

2. Content Standards G-CO.10 Prove theorems about triangles.
G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Mathematical Practices
2 Reason abstractly and quantitatively.
6 Attend to precision.

3. Vocabulary, Key Concepts, and Theorems
Legs of and isosceles triangle
Vertex angle
Base angles
Theorem 4.10 & 4.11
Corollary 4.3 & 4.4

4. Concept

5. A. Name two unmarked congruent angles.
Congruent Segments and Angles
A. Name two unmarked congruent angles.
BCA is opposite BA and A is opposite BC, so BCA  A.
___
Answer: BCA and A
Example 1

6. B. Name two unmarked congruent segments.
Congruent Segments and Angles
B. Name two unmarked congruent segments.
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BC is opposite D and BD is opposite BCD, so BC  BD.
Answer: BC  BD
Example 1

7. A. Which statement correctly names two congruent angles?
A. PJM  PMJ
B. JMK  JKM
C. KJP  JKP
D. PML  PLK
Example 1a

8. B. Which statement correctly names two congruent segments?
A. JP  PL
B. PM  PJ
C. JK  MK
D. PM  PK
Example 1b

9. Concept

10. Subtract 60 from each side. Answer: mR = 60 Divide each side by 2.
Find Missing Measures
A. Find mR.
Since QP = QR, QP  QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR.
Triangle Sum Theorem
mQ = 60, mP = mR
Simplify.
Subtract 60 from each side.
Answer: mR = 60
Divide each side by 2.
Example 2

11. Find Missing Measures
B. Find PR.
Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution.
Answer: PR = 5 cm
Example 2

12. A. Find mT.
A. 30°
B. 45°
C. 60°
D. 65°
Example 2a

13. B. Find TS.
A. 1.5
B. 3.5
C. 4
D. 7
Example 2b

14. ALGEBRA Find the value of each variable.
Find Missing Values
ALGEBRA Find the value of each variable.
Since E = F, DE  FE by the Converse of the Isosceles Triangle Theorem. DF  FE, so all of the sides of the triangle are congruent. The triangle is equilateral. Each angle of an equilateral triangle measures 60°.
Example 3

15. mDFE = 60 Definition of equilateral triangle 4x – 8 = 60 Substitution
Find Missing Values
mDFE = 60 Definition of equilateral triangle
4x – 8 = 60 Substitution
4x = 68 Add 8 to each side.
x = 17 Divide each side by 4.
The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal.
DF = FE Definition of equilateral triangle
6y + 3 = 8y – 5 Substitution
3 = 2y – 5 Subtract 6y from each side.
8 = 2y Add 5 to each side.
Example 3

16. 4 = y Divide each side by 2. Answer: x = 17, y = 4 Find Missing Values
Example 3

17. Find the value of each variable.
A. x = 20, y = 8
B. x = 20, y = 7
C. x = 30, y = 8
D. x = 30, y = 7
Example 3

18. Practice and Problem Solving
 Pg (15-22) all, (29-32) all
DUE by the end of class. What is NOT finished in class becomes homework due the following day.